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655-705 (Hard)|   Geometry|      
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MathRevolution
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A, b, c are diameters of 3 circles respectively. If ∠Z=90o, what is th Updated on: 08 Feb 2016, 00:04
Originally posted by MathRevolution on 06 Feb 2016, 18:58.
Last edited by MathRevolution on 08 Feb 2016, 00:04, edited 1 time in total.
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55% (hard)

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54% (01:33) correct 46% (01:43) wrong based on 123 sessions

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A, b, c are diameters of 3 circles respectively. If ∠Z=90o, what is the sum of the area of 3 semi-circles as above figure?

1) a^2+b^2+c^2=50
2) c^2=25


* A solution will be posted in two days.
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D
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A, b, c are diameters of 3 circles respectively. If ∠Z=90o, what is th 07 Feb 2016, 00:49
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Hi MathRevolution, the figure is not attached in the question.
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aritragster
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A, b, c are diameters of 3 circles respectively. If ∠Z=90o, what is th 03 Jul 2016, 04:23
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Could someone explain the answer as to why is it C?
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A, b, c are diameters of 3 circles respectively. If ∠Z=90o, what is th 03 Jul 2016, 10:24
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Answer is D

Lets evaluate
To calculate the sum of the area of 3 semicircles
we have
π * (a/2)^2/2 + π * (b/2)^2/2 + π * (c/2)^2/2
= π * (a^2+b^2+c^2)/8
Now lets evaluate A choice
a^2+b^2+c^2 =50
so sufficient
Lets Evaluate choice B
c^2 =25
However from question it is clear that
a^2 + b^2 =c^2
so
a^2 + b^2 =25
hence
a^2+b^2+c^2 =50
so sufficient
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A, b, c are diameters of 3 circles respectively. If ∠Z=90o, what is th 03 Jul 2016, 10:25
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Hi aritragster,

The answer is D and not C.

Total area of the 3 semicircles = pi*a^2/8 + pi*b^2/8 + pi*c^2/8 = pi*(a^2 + b^2 + c^2)/8

St1: a^2 + b^2 + c^2 = 50 --> Sufficient to calculate the area

St2: c^2 = 25
Since the triangle is right angled, c^2 = a^2 + b^2 = 25
a^2 + b^2 + c^2 = 25 + 25 = 50
Sufficient

Answer: D
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A, b, c are diameters of 3 circles respectively. If ∠Z=90o, what is th 03 Jul 2016, 18:16
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Got it. Actually I wanted to ask why it was D but typed C instead. Thanks for the explanation on the second statement. Didn't strike at once!
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A, b, c are diameters of 3 circles respectively. If ∠Z=90o, what is th 17 Jan 2022, 07:13
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If someone can explain me where I am going wrong, from the first statement I got c = 5 so 'a^2 + b^2 = 25', hence a and b can be 3 and 4 resp or '2 and underroot 21' resp and based on this differing values, final answer will differ right ?
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A, b, c are diameters of 3 circles respectively. If ∠Z=90o, what is th 30 Jan 2022, 08:11
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Dhwanii
If someone can explain me where I am going wrong, from the first statement I got c = 5 so 'a^2 + b^2 = 25', hence a and b can be 3 and 4 resp or '2 and underroot 21' resp and based on this differing values, final answer will differ right ?
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The area of circle is πr^2. Therefore the area of circle with radius c is πc^2, radius b is πb^2, and radius a is πa^2. Now since we want area of semi circles we need to divide them by 2. So essentially area of semi circle with radius c is πc^2/2, area of semi circle with radius b is πb^2/2, and area of semi circle with radius a is πa^2/2

ie, πc^2/2 + πb^2/2 + πa^2/2 or π (a^2 + c^2/2 + b^2)/2. since we are given the value of a^2 + c^2/2 + b^2 in both statements. we get the answer. so whatever individual component of a^2 or b^2 it adds ups to c^2. so we can say that both sufficient.
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